A reconstruction theorem for abelian categories of twisted sheaves

Benjamin Antieau

A reconstruction theorem for abelian categories of twisted sheaves

Algebraic Geometry 2013-11-05 v2

Authors: Benjamin Antieau

Abstract

We use an idea of Rosenberg to prove a reconstruction theorem for abelian categories of alpha-twisted quasi-coherent sheaves on quasi-compact and quasi-separated schemes X when alpha is in the Brauer group of X. By applying the work of To\"en on derived Azumaya algebras, we give a proof of C\u{a}ld\u{a}raru's conjecture.

Keywords

abelian categories twisted sheaves reconstruction theorem Brauer group quasi-coherent sheaves derived Azumaya algebras schemes

Cite

@article{arxiv.1305.2541,
  title  = {A reconstruction theorem for abelian categories of twisted sheaves},
  author = {Benjamin Antieau},
  journal= {arXiv preprint arXiv:1305.2541},
  year   = {2013}
}

Comments

14 pages; to appear in J. Reine Angew. Math.; previously entitled "Caldararu's conjecture on abelian categories of twisted sheaves"

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